Converting a set into a minimum-phase sequence

In this paper we discuss whether a given finite set of real or complex numbers can be ordered such that the derived sequence is minimum-phase. We characterize several types of sets that can be ordered in minimum-phase sequences. These sets do not span the sets of all real or complex sequences of finite length. To find the minimum-phase sequence from a given set may be computational expensive and we propose an alternative to reduce the number of operations using a list of appropriate permutations.